Mondani H, Holme P, Liljeros F (2014) Fat-Tailed
Fluctuations in the Size of Organizations: The Role of
Social Influence. PLoS ONE 9(7): e100527.
Modeling the
fat tails of size
fluctuations in
organizations
Petter Holme

Mondani H, Holme P, Liljeros F (2014) Fat-Tailed
Fluctuations in the Size of Organizations: The Role of
Social Influence. PLoS ONE 9(7): e100527.
Modeling the
fat tails of size
fluctuations in
organizations
Petter Holme

Local trade unions in Sweden, 1880–1939
-Long quiet periods
-Large jumps
F Liljeros, The complexity of social organizing, Ph.D. thesis 2001.
Typical data: time series of
sizes (not join / quit numbers)
Examples

Local trade unions in Sweden, 1880–1939
F Liljeros, The complexity of social organizing, Ph.D. thesis 2001.
Examples

Local trade unions in Sweden, 1880–1939
F Liljeros, The complexity of social organizing, Ph.D. thesis 2001.
Examples

Growth rate US firms
Buldyrev & al., J Phys I France 7 (1997), 635–650.
Examples

Growth rate Italian firms
Bottazzi, Secchi, Physica A 324 (2003), 213–219.
Examples

Examples
Growth rate Italian firms
Bottazzi, Secchi, Physica A 324 (2003), 213–219.

MHRStanley&al,1996Nature379:804–806.
Growthrate(someothersetof)USfirms
Examples

Universality

Previous models

Previous models
Economic models

Previous models
Economic models
Doesn’t fit e.g.
voluntary organizations

Physics models
Previous models

Physics models
Not without problems
either…
Previous models

Stochastic models
Previous models

Stochastic models
Previous models

Stochastic models
Original has log-
normal growth rate
distribution
Previous models

The SAF model
Assumptions
-N individuals connected in a network
-G organizations
-Each time step an agent changes
organization with probability:
Schwartzkopf, Axtell, Farmer, arxiv:1004.5397.

The SAF model
Assumptions
-N individuals connected in a network
-G organizations
-Each time step an agent changes
organization with probability:
Claims the network is
the key (still trying
just one topology)...
Schwartzkopf, Axtell, Farmer, arxiv:1004.5397.

The SAF model
Assumptions
-N individuals connected in a network
-G organizations
-Each time step an agent changes
organization with probability:
Claims the network is
the key (still trying
just one topology)...
Non-equilibrium...
Schwartzkopf, Axtell, Farmer, arxiv:1004.5397.

The SAF model
Assumptions
-N individuals connected in a network
-G organizations
-Each time step an agent changes
organization with probability:
Claims the network is
the key (still trying
just one topology)...
Non-equilibrium...
Hidden parameters...
Schwartzkopf, Axtell, Farmer, arxiv:1004.5397.

The SAF model
Schwartzkopf, Axtell, Farmer, arxiv:1004.5397.
cf. threshold models (Prof. Kertesz’s talk)

The SAF model
Schwartzkopf, Axtell, Farmer, arxiv:1004.5397.
cf. threshold models (Prof. Kertesz’s talk)

Our extended SAF model
Additional assumptions
-Trying different networks
-Organization cannot die (if the last person leaves
a new person joins)
-Attachment probability:

Results
Tent plot, ER model δ = 1.

Results
Tent plot, directed ER model δ = 1.

Results
Tent plot, scale-free networks, δ = 1.

Results
Tent plot, directed scale-free networks, δ = 1.

Results
2D grid, δ = 0

Results
2D grid, δ = 1

Results
2D grid, δ = 10

Conclusions
-The SAF model works and it is independent of the network
topology (it just needs a (strongly connected giant
component).
-The contextual influence parameter makes a difference and
can cause the loss of tentity.